Estimating Linear Relations with Errors in the Variables: The Merging of Two Approaches

  • Hans Schneeweiss

Abstract

In estimating a linear relation with errors in the variables, two main approaches can be distinguished: methods that utilize knowledge about the error variances and methods that rely on instrumental variables. This paper clarifies the relationship between these two approaches and also points to the related estimation methods in econometric models.

Keywords

Covariance Milton 

Zusammenfassung

Bei der Schätzung von linearen Beziehungen mit fehlerbehafteten Variablen lassen sich zwei Hauptansätze unterscheiden: Schätzmethoden, die Kenntnisse über die Fehlervarianzen ausnutzen und solche, die Instrumentvariablen verwenden. In diesem Aufsatz werden die Zusammenhänge zwischen beiden Ansätzen aufgezeigt und wird auf die Verwandtschaft mit den Schätzmethoden für ökonometrische Modelle hingewiesen.

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References

  1. Aigner et al., Latent variable models in econometrics. In: Handbook of Econometrics (Griliches and Intriligator, eds.), Vol.2, 1983, North-Holland, AmsterdamGoogle Scholar
  2. Anderson, T.W., Estimation of linear functional relationships: approximate distributions and connections with simultaneous equations in econometrics, Journal of the Royal Statistical Society B38, 1976, 1–36Google Scholar
  3. Fuller, W.A., Some properties of a modification of the limited information estimator, Econometrica 45, 1977, 939–954CrossRefGoogle Scholar
  4. Fuller, W.A., Properties of some estimators for the errors-in-variables model, Annals of Statistics 8, 1980, 407–422.CrossRefGoogle Scholar
  5. Goldberger, A.S., Maximum likelihood estimation of regressions containing unobservable independent variables, International Economic Review 13, 1972, 1–15CrossRefGoogle Scholar
  6. Kapteyn, A. and T. Wansbeek, Errors in variables: consistent adjusted least squares (CALS) estimation. Manuscript 1981Google Scholar
  7. Kendall, M.G. and A. Stuart, The Advanced Theory of Statistics, Vol.2, 1979, Charles Griffin, LondonGoogle Scholar
  8. Kunitomo, N., Asymptotic expansions of the distributions estimators in a linear relationship and simultaneous equations, Journal of the American Statistical Association 75, 1980, 693–700CrossRefGoogle Scholar
  9. Lindley, D.V., Regression lines and the linear functional relationship, Journal of the Royal Statistical Society, Suppl. 9, 1947, 218–244Google Scholar
  10. Madansky, W., The fitting of straight lines when both variables are subject to error, Journal of the American Statistical Association 54, 1959, 173–205CrossRefGoogle Scholar
  11. Moran, P.A.P., Estimating structural and functional relationships, Journal of Multivariate Analysis 1, 1971, 232–255CrossRefGoogle Scholar
  12. Morimune, K. and N. Kunitomo, Improving the maximum likelihood estimate in linear functional relationships for alternative parameter sequences, Journal of the American Statistical Association 75, 1980, 230–237CrossRefGoogle Scholar
  13. Nussbaum, M., Asymptotic optimality of estimators of a linear functional relation if the ratio of the error variances is known. Mathematische Operationsforschung und Statistik, Ser. Statistics 8, 1977, 173–198Google Scholar
  14. Schneeweiss, H., Modelle mit Fehlern in den Variablen, Methods of Operations Research 37, 1980, 41–77Google Scholar
  15. Schneeweiss, H. and H.-J. Mittag, Lineare Modelle mit fehlerbehafteten Daten, 1985, Physica-Verlag, Würzburg-WienGoogle Scholar
  16. Schönfeld, P., Methoden der Ökonometrie, Vol.2, 1971, Vahlen, BerlinGoogle Scholar
  17. Theil, H., Principles of Econometrics, 1971, Wiley, New YorkGoogle Scholar
  18. Tintner, G., An application of the variate difference method to multiple regression, Econometrica 12, 1944, 97–113CrossRefGoogle Scholar
  19. Tintner, G. and G. Wörgötter, Ein empirischer Test der Annahme der permanenten Einkommenshypothese von Milton Friedman, Empirica 1, 1979, 23–45CrossRefGoogle Scholar
  20. Tukey, J.W., Components in regression, Biometrics 7, 1951, 33–70CrossRefGoogle Scholar
  21. Zellner, A., Estimation of regression relationships containing unobservable variables, International Economic Review 11, 1970, 441–454.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Hans Schneeweiss
    • 1
  1. 1.MünchenGermany

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